Question: Which of the following numbers is a factor of 108? ${4,5,7,8,10}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $108$ by each of our answer choices. $108 \div 4 = 27$ $108 \div 5 = 21\text{ R }3$ $108 \div 7 = 15\text{ R }3$ $108 \div 8 = 13\text{ R }4$ $108 \div 10 = 10\text{ R }8$ The only answer choice that divides into $108$ with no remainder is $4$ $ 27$ $4$ $108$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $4$ are contained within the prime factors of $108$ $108 = 2\times2\times3\times3\times3 4 = 2\times2$ Therefore the only factor of $108$ out of our choices is $4$. We can say that $108$ is divisible by $4$.